Units of Volume

Volume: Meaning and formula.

Volume is the measure of the amount of space occupied or enclosed by any three-dimensional object by the surfaces in cubic units. As each of the measures are linear measurements, the units of volumes are derived from the units of length.

Formula:         

To find out the volume of the 3D cuboidal object, we multiply its length(l), width(b), and height(h).

In the mathematical expression:

Volume = length × width × height

V = l × b × h

Thus, we have three units of dimensions (length, width, and height), so the volume is measured in cubic units.

Let’s understand with an example:

The length of a water tanker is 8 feet and height is 7 feet and the width of the tanker is 3 feet. Find the volume of the water tanker.

By putting the values of the given dimensions in the formula.

SI units of Volume

The SI unit of volume is cubic meter (m³). However, there are also other units to measure small and large quantities of volume.

Common Units of Volume in cubic meters

Note: Each unit is 1000 times more than the previous unit. To convert the one unit to other units accordingly either multiply or divide by the number of zeros that are there in place between the units. To convert a smaller unit into a greater unit we multiply the number of zeros between the units. And to convert a greater unit into a smaller unit we divide by the number of zeros between the units.

Examples of everyday units:

• 200 ml – Juice Box.
• 500 ml – Cold drink bottle.
• 15 ml – Eye drop.
• 5l – Cooking Oil.

Relationship between the Volume, Mass and Capacity

There is a relationship that exists between capacity and volume. A liter (l) is the capacity equal to the volume of a cube that measures 10 cm³ (1 dm³) on each side.

There exists a direct relationship between the volume and mass of water. One gram equals to 1 cm³ of pure water.

Example

1. Convert into 1.76hm³ into m³

Solution:

1 hm³= 1 x 10⁶ m³

To convert the hm³ into m³, multiply the volume by 10⁶ (1,000,000) as there are two places between the units.

2. Convert the 10 m³ into liters.

Solutions:

We know 1 dm³ is equal to 1 liter. In the above example, the value is given in the m³. So, we need to first convert the unit m³ into dm³ and then have a value in liters.

1m³=1000dm³

10m³=10 × 1000dm³=100,000dm³

3. The height, width, and length of the rectangular tank are 6m, 7m, and 600 cm respectively. There is also another rectangular tank smaller in size with a volume of 20, 0000 dm³. Find out by how many cubic meters the volume of the bigger tank is more than the smaller tank.

Solutions:

Here, we have to find out the volume of the bigger rectangular tank with the given dimensions:

Length of the tank = 600 cm = 6 m (1m = 100cm)

Height of the tank = 6m.

Width of the tank = 7m.

The volume of the bigger tank:

V = 6 × 7 × 6= 252m,

The volume of the smaller tanker is given in cubic decimeters. First, we need to convert it into cubic meters.

The volume of smaller tank = 20, 0000 dm³

1m³=1000dm³

Note here, dm³ is a smaller unit than m3. Thus, we have to divide to convert the smaller unit into a bigger unit.

20,0000dm³=20,00001000m³=200m³

Now we have both the volumes in the same unit i.e. in cubic meters. We can find out the number of cubic meters by which the volume of the bigger rectangular tank exceeds the value of the smaller tank.

=252m³ – 200m³

=52m³

Thus, the volume of the bigger tank is 52m³ greater than the volume of the smaller tank.

Practice Multiple Choice Questions